Membranes and transport
Introduced| English | Meaning |
|---|---|
| lipid bilayer | An 8 nm sheet that ions cannot cross. |
| simple diffusion/ˈsɪmpl dɪˈfjuːʒn/ | simple diffusion |
| facilitated diffusion/fəˈsɪlɪteɪtɪd dɪˈfjuːʒn/ | Passive movement down a concentration or electrochemical gradient through a membrane channel or carrier protein. |
| primary active transport | primary active transport |
| secondary active transport | secondary active transport |
| Nernst equation/nɜːnst ɪˈkweɪʒn/ | An equation relating an electrode or cell potential to its standard potential, temperature and reaction quotient. |
| resting potential/ˈrestɪŋ pəˈtenʃl/ | resting potential |
| sodium-potassium pump/ˈsəʊdɪəm pəˈtæsɪəm pʌmp/ | sodium-potassium pump |
| cystic fibrosis/ˈsɪstɪk fɪˈbrəʊsɪs/ | An inherited condition caused by variants affecting the CFTR protein, leading to abnormal salt and water transport and thick mucus in organs such as the lungs. |
One question behind every drug
- Every drug target, every nerve impulse and every kidney's work comes down to one question: how does a molecule cross a membrane?
- The answer is always one of four doors, and the gradients they leave behind are a battery.
Two downhill doors, two uphill doors
- The lipid bilayer 脂双层 is an 8 nm sheet that ions cannot cross. Simple diffusion 自由扩散 suits small fat-soluble molecules; facilitated diffusion 易化扩散 uses channels or carriers, downhill, with no ATP.
- Primary active transport 原发性主动转运 burns ATP to pump uphill. Secondary active transport 继发性主动转运 lets one ion run downhill and drags another molecule uphill.
Match each door to an example.
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O₂ is small and uncharged; GLUT1 carries glucose downhill; the pump spends ATP; SGLT1 uses the Na⁺ gradient the pump made.
The Nernst equation
- At equilibrium the electrical push balances the concentration push. For ion X at 37 °C the Nernst equation 能斯特方程 gives that voltage:
- $z$ is the charge: Ca²⁺ ($z = 2$) halves the slope, and Cl⁻ ($z = -1$) flips the sign.
For K⁺ (140 mM in, 5 mM out), $E_K$ at 37 °C is about —
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E = 61.5 × log10(5/140) = 61.5 × (−1.447) = −89.0 mV.
Worked example: four ions, four voltages
- K⁺ (140 in, 5 out): $61.5\log_{10}(5/140) = -89.0$ mV. Na⁺ (12 in, 145 out): $+66.6$ mV.
- Cl⁻ (10 in, 110 out, $z = -1$): $-64.0$ mV. Ca²⁺ (100 nM in, 1.2 mM out, $z = 2$): $+125.4$ mV.
Ca²⁺ is 100 nM inside and 1.0 mM outside. What is $E_{Ca}$ at 37 °C?
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The ratio is 1.0 mM / 100 nM = 10⁴, so E = (61.5/2) × 4 = 123 mV. Forget z = 2 and you get 246 mV.
The resting potential
- Several ions leak at once, so Goldman–Hodgkin–Katz weights each by permeability. With $P_K : P_{Na} : P_{Cl} = 1 : 0.04 : 0.45$ the resting potential 静息电位 is −67.3 mV.
- That is about 20 mV above $E_K$, because Na⁺ leaks in. The sodium-potassium pump 钠钾泵 (3 Na⁺ out, 2 K⁺ in, 1 ATP) keeps the battery charged.
Ion ratios to resting voltage
Move the outside ion levels and the Na⁺ permeability; watch each Nernst bar move and the Goldman resting voltage follow, and see why it stays close to the K⁺ equilibrium voltage.
Why does the resting potential sit close to $E_K$ rather than $E_{Na}$?
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GHK weights each ion by permeability. $P_K$ dominates, so $V_m$ = −67 mV, about 20 mV above $E_K$ = −89 mV; the small Na⁺ leak makes the difference.
Worked example: hyperkalaemia
- A (fictional) patient's blood K⁺ doubles from 5 to 10 mM. $E_K$ moves by $61.5\log_{10}2 = +18.5$ mV, from −89 to −71 mV.
- The resting potential moves less, from −67 to −60 mV, because K⁺ is only part of the weighted sum. Still, heart cells sit closer to threshold: raised potassium is a cardiac emergency.
In hypokalaemia, blood K⁺ falls to 2.5 mM (140 mM inside). What is $E_K$ at 37 °C?
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E = 61.5 × log10(2.5/140) = 61.5 × (−1.748) = −107.5 mV: halving outside K⁺ moves $E_K$ 18.5 mV more negative.
Worked example: the chloride door that misfolds
- The commonest cystic fibrosis 囊性纤维化 variant (ΔF508) deletes one amino acid from a Cl⁻ channel. The channel misfolds and never reaches the membrane.
- Cl⁻ cannot leave, so less salt reaches the airway surface and less water follows it. The surface dries and mucus cannot clear: one fold, one door, one disease.
In ΔF508 cystic fibrosis, what is the first defect?
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One deleted phenylalanine misfolds the channel; everything after it (salt, water, mucus) follows from that one door.
Put the cystic fibrosis chain in order.
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Water follows salt by osmosis, so a missing chloride door ends as dry, sticky mucus. Drugs that help the channel fold act at the first step.
Three common slips
- Nernst for the resting potential. Nernst describes one ion at equilibrium; with several ions leaking, use GHK.
- Forgetting $z$. Ca²⁺ has $z = 2$, so its slope is 30.75 mV per decade, not 61.5.
- "Channels are active." Only pumps burn ATP; a channel only lets ions run downhill.
An open ion channel is active transport, because ions move through it quickly.
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Speed is not the test. A channel only lets ions move down their gradient; active transport spends ATP (or another gradient) to move them uphill.
Recap
- Four doors: simple and facilitated diffusion downhill; primary and secondary active transport uphill.
- $E_X = (61.5/z)\log_{10}([X]_{out}/[X]_{in})$ mV at 37 °C.
- GHK gives −67 mV at rest, held by 3 Na⁺ out and 2 K⁺ in per ATP.